Stats Without Walls Methods Guide

Descriptives and graphs

Use it for every variable before any test, and as the answer when the question is only "what does it look like".

1. Exploration › Descriptives: pick the numeric columns; add a grouping column to describe each group separately. Tick Frequency tables for nominal and ordinal variables. Quartile method: the course's halves rule or R's type 7.
2. Read mean and median together: far apart means skew. The SD is the typical distance from the mean; the IQR is the middle half.
3. Graph › Histogram for shape, Graph › Boxplot by group for comparisons, Graph › Bar Plot or Graph › Pie Chart for categories, Graph › QQ Plot to judge normality.

Report: n, mean (SD) or median [IQR] for skewed data, and counts (percent) for categories. One table per paper is normal: "Table 1".

One group against a claimed value: one-sample t test

Use it when one numeric variable is compared with a known or claimed value (the mean commute is 30 minutes; the mean GPA is 3.0).

1. T-Tests › One Sample T-Test. Data: from a column, or type the mean, SD and n. Enter the Test value; choose the hypothesis direction.
2. Tick Confidence interval and Effect size (Cohen's d).
3. Read: t, df and p; the interval for the mean; the conclusion line names H₀ and Hₐ and the decision at α.

Assumption: roughly normal data, or n of 30 or more. The card says which applies. Otherwise Nonparametric › Wilcoxon signed-rank and sign test (paired) with "compare variable 1 with a constant".

Report: t(39) = 2.14, p = .039, d = 0.34, 95% CI [0.02, 0.61] (the app writes this line).

One proportion against a claimed value: z test, or the exact binomial test

1. Frequencies › One proportion: z test when the conditions hold: np₀ and n(1 − p₀) both at least 10. The card checks them, shows SE₀ = √(p₀(1 − p₀)/n), z = (p̂ − p₀)/SE₀, the p-value, and the exact binomial p-value underneath as a check. Data: a yes or no column (name the level to test), or type the count of successes and n. Enter the Test value (the claimed proportion).
2. Frequencies › 2 Outcomes: Binomial test when the conditions fail, or whenever you want the exact answer first: the exact test needs no sample-size condition. The same dialog can show the z test underneath.
3. Tick Confidence intervals; the Interval method offers Wilson (recommended) and the course's Wald. Read the p-value and the interval.

Category counts against a claimed split: chi-square goodness of fit

1. Frequencies › N Outcomes: chi-square Goodness of fit. Data: a category column, or typed counts.
2. Expected: Equally likely, or type the proportions (or counts) in the level order shown.
3. Read χ², df and p, and the check that every expected count is at least 5; combine small levels if not.

Two different groups, a number: independent-samples t test

Use it when one numeric outcome is compared between two separate groups (treatment and control; men and women; two campuses).

1. Data: one numeric column and one grouping column with exactly two levels (or two numeric columns, one per group; or typed means, SDs and n).
2. T-Tests › Independent Samples T-Test. Welch's t (unequal variances) is the default and the right default; tick Student's pooled t only if the course asks for it.
3. Tick Mean difference, Confidence interval, Effect size (Cohen's d) and Descriptives plots.
4. Read: the difference and its interval first, then t, df and p, then the conclusion. The assumption lines report sample sizes and shape.

If the data are skewed with small groups: Nonparametric › Mann-Whitney U (two groups). With no assumptions at all: Advanced › Permutation test (design: two independent groups).

Report: t(37.2) = 2.46, p = .019, d = 0.78, 95% CI of the difference [0.9, 9.6]. Welch's df is fractional; that is correct.

Two different groups, a yes or no: two-proportion z test or a 2 by 2 table

1. Frequencies › Two proportions: z test. Data: a yes or no column and a two-level group column (name the success level), or type successes and n for each group.
2. Read the difference in proportions with its interval, z and p. The card checks that each group has at least 10 successes and 10 failures.
3. Small counts: Frequencies › Contingency Tables: Independent Samples with the same two columns; tick Fisher's exact test (2 by 2) and choose its direction. Tick Odds ratio and relative risk (2 by 2) for the risk ratio and odds ratio with intervals; relative risk needs a cohort (groups defined before the outcome), the odds ratio is valid in case-control designs too.

The same people measured twice: paired t test

Use it for before and after, pre-test and post-test, or matched pairs. The analysis is of the differences.

1. Data: two numeric columns, one row per person (before, after).
2. T-Tests › Paired Samples T-Test; tick Confidence interval, Effect size and Histogram of differences.
3. Read the mean difference and its interval, then t, df = n − 1 and p. The histogram of differences is the assumption check.

Skewed differences or ratings: Nonparametric › Wilcoxon signed-rank and sign test (paired). A yes or no measured twice: Advanced › McNemar test (paired yes or no), which uses only the people who changed.

Three or more different groups: one-way ANOVA

1. Data: one numeric column and one grouping column with three or more levels.
2. ANOVA › One-Way ANOVA. Keep Assume equal (Fisher's) and add Don't assume equal (Welch's); tick Post-Hoc Tests: Tukey, Descriptives table, Descriptives plots and Levene's test of equal variances.
3. Read F, df and p for "any difference", then the Tukey table for which pairs differ (its p-values are already adjusted for the number of comparisons). η² on the APA line is the share of variance explained.
4. If Levene's p is small or the largest SD is more than twice the smallest, read Welch's F instead.

Skewed data or ordinal ratings: ANOVA › Kruskal-Wallis (three or more groups).

Report: F(3, 36) = 4.21, p = .012, η² = .26, then each Tukey pair that differs with its adjusted p and mean difference.

The same people measured three or more times: repeated-measures ANOVA

1. Data in wide form: one column per time or condition (week1, week4, week8), one row per person. Optionally a between-subjects group column for a mixed design.
2. ANOVA › Repeated Measures and Mixed ANOVA: list the Repeated measures columns, in order; tick Pairwise paired t-tests with Holm correction.
3. Read the within-subjects F (with the sphericity note), the group and interaction rows in a mixed design, and the Holm-adjusted pairs.

Ratings or skewed data: ANOVA › Friedman (nonparametric repeated measures), with Kendall's W as the effect size.

Two numbers: correlation

1. Graph › Scatter Plot first. A relationship that is curved, or driven by one point, is not a correlation question.
2. Regression › Correlation Matrix: pick the variables; tick Pearson, Report significance and Scatter plots (pairs). Add Spearman for ratings, ranks or outliers.
3. Read r (direction and strength, −1 to 1), its p for "different from zero", and the scatterplot. r² is the share of variance shared.

Two categories: chi-square test of independence

1. Data: two category columns (major by employment), or a typed table of counts.
2. Frequencies › Contingency Tables: Independent Samples; tick chi-square, Observed counts, Expected counts and Row percentages (the percentages are what you interpret).
3. Read χ², df = (rows − 1)(columns − 1) and p; the card checks that every expected count is at least 5. For a 2 by 2 table with small counts tick Fisher's exact test (2 by 2).

Effect size: for a 2 by 2 table report the risk ratio or odds ratio with its interval (tick Odds ratio and relative risk); for larger tables describe the row percentages that differ most.

A number across groups

That is a group comparison: see two groups or three or more groups. T-Tests › Which test? routes it.

A number from one number: simple linear regression

1. Regression › Linear Regression: outcome y and predictor x. Tick Confidence interval for coefficients, R and R squared (Model Fit), Residual plots and Q-Q plot of residuals. Enter values under Predict at x = to get predictions with intervals; tick the bands on the graph.
2. Read the equation ŷ = b₀ + b₁x, the slope's interval and p (H₀: β₁ = 0), and R². The residual plot should be a shapeless cloud; a curve or a fan means the line is the wrong model or the spread changes with x.
3. Predict only inside the range of x you observed.

Report: b = 0.082, 95% CI [0.03, 0.13], t(38) = 3.21, p = .003, R² = .21; say the units ("each extra hour of study predicts 0.08 GPA points").

Before and after

Two measurements of the same units: the paired t test (numbers), Wilcoxon (ratings), McNemar (yes or no). Three or more measurements: repeated-measures ANOVA or Friedman. With a control group, ANCOVA on the post-test with the pre-test as covariate.

A series over time: trend, season, forecast

1. Data: one row per time point in order, a numeric column; a date or period column is optional.
2. Advanced › Time Series. Set the Seasonal period (12 monthly, 4 quarterly, 7 daily). Tick Decomposition, Autocorrelation (ACF and PACF), Linear trend and Durbin-Watson and the Holt forecast with the steps ahead you need.
3. Read the decomposition (trend, seasonal, remainder), the trend slope per period, and the forecast with its band. Durbin-Watson near 2 means the residuals are not autocorrelated; far from 2 means the simple trend line understates uncertainty.

How many people do I need?

1. For a survey estimate: distrACTION › Sample size for a margin of error. Pick a mean or a proportion, the margin of error you can accept, and a guess for p (0.5 is the safe guess) or s.
2. For a test: Advanced › Power and Sample Size. Pick the test, the effect size you want to detect (a difference that would matter, not the one you hope for), α, and a target power of 0.80 or 0.90; read n per group. Or enter n and read the power you have.

Pilot data give the SD; the literature gives the smallest effect worth finding. Plan for drop-out by inflating n. A study that is underpowered cannot distinguish "no effect" from "too small to see", which is the most common reason a null result is uninformative.